All simulators
c-Components & Tian's Criterion
Toggle arrows and hidden-confounder edges; c-components and the identification verdict update live.
Day 56: Identification Algorithms & Non-Identifiable Queriesc-component of X: {X, Y}; children of X: {M}.
No child of X shares its c-component: identified. P(v | do(x)) = P(v) · Σₓ Q[S_X] / Q[S_X].
No child of X shares its c-component: identified. P(v | do(x)) = P(v) · Σₓ Q[S_X] / Q[S_X].
DIRECTED EDGES
BIDIRECTED EDGES (UNMEASURED CONFOUNDING)
c-components: {W} {Z} {X, Y} {M}
Switch arrows and bidirected (unmeasured-confounding) edges on and off. Nodes in the same c-component share a colour. Tian's criterion: the effect of X on all other variables is identified exactly when no child of X lies in X's c-component. The napkin shows that P(y | do(x)) for one outcome can still be identified when the criterion fails.